Death claws

Get a high small guns and high sneak, and repair levels like 75 or 100, and use the hunting rifle, sniper rifle or combat shot gun on them, try for the
" Critical Sneak Attack ".

I have both high level small guns, sneak and repair and I use lincolns repeater rifle found at the museum of history. [ lincolns repeater rifle is a winchester that uses 44 magnum ammo, takes heads clean off! ]

Trying to avoid them could be tricky, it depends on your sneak and perception levels,[ if you can see them before they see you you could back track away or go around ] stay away from old olney and the terror claw caves for now until you get good levels in the above mentioned levels. Also if you have done the part of the main quest " Waters Of Life " the enclave show up throughout the wasteland and often use terror claws as watchdogs so watch out.

Use the Dart Gun. One hit cripples both legs and slows them down quite a bit, allowing you to back off and use an assault rifle or Combat Shotgun to finish the job. Above all else, try to avoid coming in close to them. If you have no other choice, use the Shiskabob or the Combat Shotgun to take him down fast in VATS.

If you focused around big guns (I never do...) Miniguns and Flamers will probably work well too.

Even better: IF you've found the crashed Space Ship, the Alien Blaster is godly. A full clip can take out a Super Mutant Behemoth, so it should make a Deathclaw a funny memory.

Hope this helps.

There is a gun called the Alien Blaster and if you head north of the minefield and find the downed power line you will pick up a singnal. Turn it on and follow it and you will get the gun and 120 rounds by the alien.

There is a gun well it's the alien blaster but upgraded it's called the firelance it does less damage than the normal alien blaster but every time you shoot someone. It has a chance of 94% hitting a critical hit so it could hit high plus if your laser wepon skills were 100 and you hit a critical hit it could make a replacement for the fat man. It also does the flame damage like the flamer or shishkabab. It can be found most can be found at the front of the Super-Duper Mart either a raider has got it or it's stuck in a wall or the ground. You could find it anywhere but mostly the Super-Duper Mart.
I would suggest using Dogmeat for this.

I play on Very Hard difficulty and I found the easiest to kill 1 of them is through the Gauss Rifle. You can find one of those beauties in the DLC Operation Anchorage. I also use the Chinese Stealth suit and shoot from afar. They wont catch onto you if you're far enough away and it does godly amounts of damage if you have you're sneak skill and energy weapons skills up maxed. Hope this helps

Well the best way to kill a deathclaw is to cripple it's legs to slow it down with any weapon, and then do a few headshots, depending on your level.

The best way to avoid one is if you see one, don't go near it.